An Analysis of Frequency-Temperature Relations of At-Cut Quartz Crystal Resonators By Finite Element Method With Comsol

In order to study the frequency-temperature relations of AT-cut quartz crystal resonators, vibrations of the quartz crystal blank in the temperature field is analyzed by incremental thermal field theory. With the incremental thermals field equations, the mathematical models of thermal expansion coefficients and temperature, thermal elasticity coefficient and temperature, and density temperature coefficient and temperature are used. The thermal coefficient function model of quartz crystal is established by using the parametric model with the finite element simulation software COMSOL, and the impedance relations and harmonic frequency are analyzed at a given ambient temperature.